For the month of May, London's most iconic department store will host a Prada 'takeover', extending from its forty Brompton Road windows, to a pop-up store, museum-worthy exhibition and grand Milanese café.

Uniting Mrs Prada's fashion, art, architecture and cinema spheres of influence, the Spring showcase is the monolithic store's latest shopping spectacle, following the house of Dior's treatment last year and Chanel in 2011. It's a wildly successful brand-building consumer concept that has since sparked a string of retail retrospectives internationally - from Le Bon Marche's recent Proenza Schouler exhibition, to Barney's current sponsorship of Dries Van Noten's 'Inspirations' at the Musée des Arts Décoratifs.

And while the Knightsbridge windows (also commandeered by Wallpaper* last October with highlights from our Handmade exhibitions) and pop-up boutique on the ground floor showcase an exclusive collection of Prada archive re-issues – the leather fringe dress is indeed back, along with 2009's gladiator Mary Janes – the fourth floor exhibition is without doubt the main attraction.

To bring Mrs Prada's 'museum within a museum' concept to life, the creative director enlisted regular collaborator, 2x4 founding partner, Michael Rock to manifest the grandiose exhibit of intertwined Prada obsessions.

Inside, the spectacle opens with archive curios from Mrs Prada's grandfather Mario Prada, and his brother Martino's original Milan store. Founded in 1913 within the Galleria Vittorio Emanuele II shopping arcade, the store's original tortoiseshell hair combs lie next to gentleman's manicure sets and time-warn silk clutch bags, echoing another era of the brand's rich history.

However, introductions made, Pradasphere was not designed as a retrospective, so from there visitors are quickly transplanted into the now. Crossing the vast room's moss and ebony checkerboard carpet (referencing the brand's marble tiled stores), six expansive vitrines, replicating those from the original Galleria store, house myriad ensembles grouped into central themes that have defined Mrs Prada's work.

Accessories are similarly arranged in a case called 'Specimens', along with mounted examples of the brand's 'materiality', putting the Prada atelier's exquisite craftsmanship under the microscope. Highlights include mink intarsias, mother of pearl embroideries, and silicone-dipped Guipure lace, all protected under glass. Vernon Panton's Clover Leaf sofas, launched at the Salone del Mobile last month, offer a seat for contemplation.

Next, large format books document the visual Prada universe from show venues to campaign stars, while additional displays are dedicated to show invitations, a model of the Seoul Transformer, and Fondazione Prada's new Milan headquarters designed by OMA.

Rounding up the house's cross-disciplinary pursuits is 'Evolution 1': a digital wall that tracks the brand's recent history, from a catwalk video of Mrs Prada's first collection, to a timeline of special projects that include film collaborations with directors Roman Polanski and Wes Anderson, and architectural projects with Rem Koolhaas and Herzog & de Meuron. The digital concept has then been extended to a video catwalk wall - organised by colour, rather than season, concealing a VIP shopping salon behind Prada's model army.

In London from New York, curator Michael Rock walks us through Pradasphere's concept to realisation…

Wallpaper*: What was the initial project brief from Miuccia Prada?
Michael Rock: The inspiration was a natural history museum of Prada, because we thought that the 19th century department store was a kind of museum in itself, so it was an attempt to be contextual. We had this image in mind of the way that the dinosaurs look.

What was the take home message that you wanted to extend to visitors?
It was about trying to tell the story of what makes Mrs Prada's work so consistent, because it's not consistent visually, so it has to be consistent in another way, as she's often exploring lots of things at the same time. What I think makes her work so specific is that she's always questioning. She has her own questions and she's working them out through design. The best design always does that. You really feel an inquisitive mind at work.

How long have you been working on the exhibition?
Not as long as you think. Time's compressed in the Prada world. It's probably been about a year in the making. We had worked with Mrs Prada on the Prada book about four years ago and that worked as the foundation for this - all the research had been done. She's been super involved in every stage of it, selecting all the looks and making the final edits.

Tell us about the restaurant space?
Rather than make a fake Milanese café we just brought Marchesi in. It's a special place to her, a classic, iconic place. To bring that here is part of the experience. The space is normally a terrace, so not in use. All the lights, display cabinets, palms and furnishings were added.

What were the main challenges that you faced?
Time and the vast amount of stuff. The archive is huge. When we were doing this, they filled the whole fashion show area with racks full of clothes, and we started to developed a series of themes and she pulled out clothes to match them. It was a very back and forth process between theory and practice.

Is this the exhibition's only stop?
It's under consideration. Originally we were thinking just for here but it lends itself to travel because it's very contained. We have a plan for it, so I think that now we'll explore it.

What's next for you?
Five weeks from now we open a new show in Venice for the Fondazione. Then it's the next addition of the Miu Miu member's club - to be disclosed soon. In July, I'll take a holiday.